Related papers: Bayesian Optimization with Exponential Convergence

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…

Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…

Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the hyper-parameter…

We propose a canonical form of the experimental optimization problem and review the state-of-the-art methods to solve it. As guarantees of global convergence to an optimal point via only feasible iterates are absent in these methods, we…

Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to…

Bayesian optimization is an advanced tool to perform ecient global optimization It consists on enriching iteratively surrogate Kriging models of the objective and the constraints both supposed to be computationally expensive of the targeted…

We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected…

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al.…

Bayesian optimization (BO) developed as an approach for the efficient optimization of expensive black-box functions without gradient information. A typical BO paper introduces a new approach and compares it to some alternatives on simulated…

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…

Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed…

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…

This paper presents a method called sampling-computation-optimization (SCO) to design batch Bayesian optimization. SCO does not construct new high-dimensional acquisition functions but samples from the existing one-site acquisition function…